my son has to draw a figure with an area of 63 and a perimeter of 32.how do he go about doing it?
what kind of figure?
circle?, square?, triangle? , rectangle?, ......
Area of a rectangle = length times width
The factors of 63 are:
3 * 21
9 * 7
Perimeter = 2 times length plus 2 times width
The rectangle can't be 3 by 21 since its perimeter would be 6 + 42
The dimensions must be 9 by 7.
(2 * 9) + (2 * 7) = 18 + 14 = 32
He needs to draw a rectangle that measures 9 by 7.
To help your son draw a figure with an area of 63 and a perimeter of 32, we can start by breaking down the problem into smaller steps:
Step 1: Understand the question
- The figure should have a specific area (63) and perimeter (32).
Step 2: Identify the possible figure types
- There are several possible figures that can meet these requirements, such as rectangles, squares, or even irregular shapes.
Step 3: Determine the figure type
- To narrow down the options, we can use the formulas for area and perimeter of different figures.
Step 4: Calculate the dimensions
- Calculate the dimensions of the figure using the given area and perimeter.
For example, let's consider the figure to be a rectangle:
Step 1: Understand the question
- The figure should have an area of 63 and a perimeter of 32.
Step 2: Determine the figure type
- Since we have a rectangle, we can use the formulas for area and perimeter of a rectangle: Area = length × width and Perimeter = 2(length + width).
Step 3: Calculate the dimensions
- Let's assume the length of the rectangle is L and the width is W.
- We have two equations based on the given area and perimeter:
- Equation 1: L × W = 63 (area equation)
- Equation 2: 2(L + W) = 32 (perimeter equation)
Step 4: Solve the equations
- We can solve these equations simultaneously to find the values of L and W.
- Rearrange Equation 2 to get L + W = 16.
- Use this in Equation 1 to substitute L + W with 16: L × (16 - L) = 63.
- Simplify this equation: 16L - L^2 = 63.
- Rearrange it to form a quadratic equation: L^2 - 16L + 63 = 0.
- Solve this equation using factoring or the quadratic formula to find the possible values of L.
- After obtaining the value(s) of L, substitute it back into Equation 2 to find the corresponding value(s) of W.
Following these steps will help your son find the dimensions of the rectangle or other figures that satisfy the given conditions. Keep in mind that there may be multiple solutions or different figure types that can fulfill the requirements.